Parametric solution of p-norm semiparametric regression model

Abstract

In this paper, using the kernel weight function, we obtain the parameter estimation of p-norm distribution in semi-parametric regression model, which is effective to decide the distribution of random errors. Under the assumption that the distribution of observations is unimodal and symmetry, this method can give the estimates of X, S and σ. Finally, three experiment are constructed to explain this method. When there is model error, the traditional least squares method is estimated to be distorted. In the first experiment, the parameter has a true value of 1, and the least squares method and the proposed new method are estimated to be 0.4883 and 0.9898 respectively. The proposed method is applicable to the different distribution of random errors. In the example of this article, it has also been reflected.